How lazy evaluation forced Haskell to be pure

Question

I remember seeing a presentation in which SPJ said that lazy evaluation forced them to keep Haskell pure (or something along that line). I often see many Haskellers saying the same.

So, I would like to understand how lazy evaluation strategy forced them to keep Haskell pure as opposed to a strict evaluation stragegy ?

Answer 1

It's not so much that lazy evaluation led to purity; Haskell was pure to begin with. Rather, lazy evaluation forced the designers of the language to keep the language pure.

Here is a relevant passage from the article A History of Haskell: Being Lazy with Class:

Once we were committed to a lazy language, a pure one was inescapable. The converse is not true, but it is notable that in practice most pure programming languages are also lazy. Why? Because in a call-by-value language, whether functional or not, the temptation to allow unrestricted side effects inside a “function” is almost irresistible.

Purity is a big bet, with pervasive consequences. Unrestricted side effects are undoubtedly very convenient. Lacking side effects, Haskell’s input/output was initially painfully clumsy, which was a source of considerable embarrassment. Necessity being the mother of invention, this embarrassment ultimately led to the invention of monadic I/O, which we now regard as one of Haskell’s main con- tributions to the world, as we discuss in more detail in Section 7.

Whether a pure language (with monadic effects) is ultimately the best way to write programs is still an open question, but it certainly is a radical and elegant attack on the challenge of programming, and it was that combination of power and beauty that motivated the designers. In retrospect, therefore, perhaps the biggest single benefit of laziness is not laziness per se, but rather that laziness kept us pure, and thereby motivated a great deal of productive work on monads and encapsulated state.

(my emphasis)

I also invite you to listen to 18'30'' of Software Engineering Radio podcast #108 for an explanation by the man himself. And here is a longer but relevant passage from SPJ's interview in Peter Seibel's Coders at Work:

I now think the important thing about laziness is that it kept us pure. [...]

[...] if you have a lazy evaluator, it’s harder to predict exactly when an expression is going to be evaluated. So that means if you want to print something on the screen, every call-by-value language, where the order of evaluation is completely explicit, does that by having an impure “function”—I’m putting quotes around it because it now isn’t a function at all—with type something like string to unit. You call this function and as a side effect it puts something on the screen. That’s what happens in Lisp; it also happens in ML. It happens in essentially every call-by-value language.

Now in a pure language, if you have a function from string to unit you would never need to call it because you know that it just gives the answer unit. That’s all a function can do, is give you the answer. And you know what the answer is. But of course if it has side effects, it’s very important that you do call it. In a lazy language the trouble is if you say, “f applied to print "hello",” then whether f evaluates its first argument is not apparent to the caller of the function. It’s something to do with the innards of the function. And if you pass it two arguments, f of print "hello" and print "goodbye", then you might print either or both in either order or neither. So somehow, with lazy evaluation, doing input/output by side effect just isn’t feasible. You can’t write sensible, reliable, predictable programs that way. So, we had to put up with that. It was a bit embarrassing really because you couldn’t really do any input/output to speak of. So for a long time we essentially had programs which could just take a string to a string. That was what the whole program did. The input string was the input and result string was the output and that’s all the program could really ever do.

You could get a bit clever by making the output string encode some output commands that were interpreted by some outer interpreter. So the output string might say, “Print this on the screen; put that on the disk.” An interpreter could actually do that. So you imagine the functional program is all nice and pure and there’s sort of this evil interpreter that interprets a string of commands. But then, of course, if you read a file, how do you get the input back into the program? Well, that’s not a problem, because you can output a string of commands that are interpreted by the evil interpreter and using lazy evaluation, it can dump the results back into the input of the program. So the program now takes a stream of responses to a stream of requests. The stream of requests go to the evil interpreter that does the things to the world. Each request generates a response that’s then fed back to the input. And because evaluation is lazy, the program has emitted a response just in time for it to come round the loop and be consumed as an input. But it was a bit fragile because if you consumed your response a bit too eagerly, then you get some kind of deadlock. Because you’d be asking for the answer to a question you hadn’t yet spat out of your back end yet.

The point of this is laziness drove us into a corner in which we had to think of ways around this I/O problem. I think that that was extremely important. The single most important thing about laziness was it drove us there.

(my emphasis)

Answer 2

I think the answer by Jubobs already sums it up nicely (with good references). But, in my own words, what I think SPJ and friends are referring to is this:

Having to go through this "monad" business can be really inconvenient at times. The sheer volume of questions on Stack Overflow asking "how do I just remove this IO thing?" is testament to the fact that sometimes, you really really want to just print out this one value right here — usually for the purposes of figuring out what the actual **** is going on!

In an eager language, it would be sorely tempting to just start adding magic impure functions that let you do impure stuff directly, like in other languages. No doubt you'd start with small things at first, but slowly you slide down this slippery slope, and before you know it, effects are all over the place.

In a lazy language like Haskell, this temptation still exists. There are many times when it would be really helpful to be able to just quickly sneak this one little effect in here or there. Except that because of laziness, adding effects turns out to be almost utterly useless. You can't control when anything happens. Even just Debug.trace tends to produce utterly incomprehensible results.

In short, if you're designing a lazy language, you really are forced to come up with a coherent story for how you're handling effects. You can't just go "meh, we'll pretend this function is just magic"; without the ability to control effects more precisely, you'll instantly end up in a horrible mess!

TL;DR In an eager language, you can get away with cheating. In a lazy language, you really have to do things properly, or it just plain doesn't work.

And that is why we hired Alex — wait, wrong window...

Answer 3

It depends by what you mean for "pure" in this context.

• If for pure you mean as in purely functional, then what @MathematicalOrchid is true: with lazy evaluation you wouldn't know in which sequence impure actions are executed and hence you wouldn't be able to write meaningful programs at all and you are forced to be more pure (using the IO monad).

  However I find this not really satisfying in this case. A true functional language already separates pure and impure code, so even a strict one should have some kind of IO.

• However it's possible that the statement is more broad and refers to pure in the fact that you are able to express more easily, in a more declarative, compositional and yet efficient way the code.

Looking at this answer which makes exactly the statement you are citing it links to the article Why Functional Programming Matters by Hughes which is probably the one you are talking about.

The paper shows how higher order functions and lazy evaluation allow to write more modular code. Note that it does not say anything about purely functional etc. The point it is making is about being more modular and more declarative without losing in efficiency.

The article provides some examples. For example the Newton-Raphson algorithm: in a strict language you have to combine together the code that computes the next approximation and the one that checks if you obtained a good enough solution.

With lazy evaluation you can generate the infinite list of approximations in a function and call this from an other function that returns the first good enough approximation.

---

In Thinking Functionally with Haskell Richard Bird makes precisely this point. If we look at Chapter 2, exercise D:

Beaver is an eager evaluator, while Susan is a lazy one.

[...]

What alternative might Beaver prefer to head . filter p . map f?

And the answer says:

[...] Instead of defining first p f = head . filter p . map f, Beaver might define

first :: (b -> Bool) -> (a -> b) -> [a] -> b
first p xs | null xs = error "Empty list"
           | p x = x
           | otherwise = first p f (tail xs)
           where x = f (head xs)

The point is that with eager evaluation most functions have to be defined using explicit recursion, not in terms of useful component functions like map and filter.

So pure here means that allows declarative, compositional and yet efficient definitions while with eager evaluation using declarative and compositional definitions can lead to unnecessarily inefficient code.